Evaluate numerically to high precision:

The precision of the output tracks the precision of the input:

Evaluate for complex arguments:

Evaluate CosIntegral efficiently at high precision:

CosIntegral threads elementwise over lists and matrices:

Compute worst-case guaranteed intervals using Interval and CenteredInterval objects:

Or compute average-case statistical intervals using Around:

Compute the elementwise values of an array:

Or compute the matrix CosIntegral function using MatrixFunction:

Value at a fixed point:

Values at infinity:

Find a local maximum as a root of :

Plot the CosIntegral function:

Plot the real part of :

Plot the imaginary part of :

CosIntegral is defined for all positive real values:

Complex domain:

CosIntegral is not an analytic function:

Nor is it meromorphic:

CosIntegral is neither non-decreasing nor non-increasing:

CosIntegral is not injective:

CosIntegral is not surjective:

CosIntegral is neither non-negative nor non-positive:

It has both singularity and discontinuity in (-∞,0]:

CosIntegral is neither convex nor concave:

First derivative:

Higher derivatives:

Formula for the derivative:

Indefinite integral of CosIntegral:

Definite integral of CosIntegral over its entire real domain:

More integrals:

Taylor expansion for CosIntegral around :

Plots of the first three approximations for CosIntegral around :

Find series expansion at infinity:

CosIntegral can be applied to power series:

Use FullSimplify to simplify expressions containing the cosine integral:

Use FunctionExpand to express CosIntegral through other functions:

Simplify expressions to CosIntegral:

Argument simplifications:

Primary definition of CosIntegral:

Series representation of CosIntegral:

CosIntegral can be represented in terms of MeijerG:

CosIntegral can be represented as a DifferentialRoot:

TraditionalForm formatting: